9514 1404 393
Answer:
153 square units
Step-by-step explanation:
The figure is drawn in the attachment with some lengths and points labeled.
The figure can be considered to have an area that is the sum of the areas of rectangle ABFE and triangle FGH, with the area of triangle BCD subtracted.
That area is ...
A = area(ABFE) +area(FGH) -area(BCD)
= (15)(9) +(1/2)(9)(6) -(1/2)(6)(3)
= 135 +27 -9 = 153 . . . square units
Answer:
m = 11/36
Step-by-step explanation:
6/7 m - 1/7 = 5/ 42
Multiply each side by 42 to clear the fractions
42(6/7 m - 1/7) = 5/ 42 *42
36m - 6 = 5
Add 6 to each side
36m -6+6 = 5+6
36m = 11
Divide each side by 36
36m/36 = 11/36
m= 11/36
Answer:
5a. -0.4 m/s²
5b. 290 m
6. 12.9 s
7. 100 s
8. 17.2 km/hr
Step-by-step explanation:
5. "While approaching a police officer parked in the median, you accelerate uniformly from 31 m/s to 27 m/s in a time of 10 s.
a. What is your acceleration?
b. How far do you travel in that time?"
Given:
v₀ = 31 m/s
v = 27 m/s
t = 10 s
Find: a and Δx
v = at + v₀
(27 m/s) = a (10 s) + (31 m/s)
a = -0.4 m/s²
Δx = ½ (v + v₀) t
Δx = ½ (27 m/s + 31 m/s) (10 s)
Δx = 290 m
6. "If a pronghorn antelope accelerates from rest in a straight line with a constant acceleration of 1.7 m/s², how long does it take for the antelope to reach a speed of 22 m/s?"
Given:
v₀ = 0 m/s
v = 22 m/s
a = 1.7 m/s²
Find: t
v = at + v₀
(22 m/s) = (1.7 m/s²) t + (0 m/s)
t = 12.9 s
7. "A 1200 kg airplane starts from rest and moves forward with a constant acceleration of 5 m/s² along a runway that is 250 m long. How long does it take the plane to travel the 250 m?"
Given:
v₀ = 0 m/s
a = 5 m/s²
Δx = 250 m
Find: t
Δx = v₀ t + ½ at²
(250 m) = (0 m/s) t + ½ (5 m/s²) t²
t = 100 s
8. "During a marathon, a runner runs the first 10 km in 0.58 hours, the next 10 km in 0.54 hours and the last 10 km in 0.62 hours. What is the average speed of the runner during that marathon?"
This isn't a constant acceleration problem, so there's no need for a chart.
Average speed = total distance / total time
v = (10 km + 10 km + 10 km) / (0.58 hr + 0.54 hr + 0.62 hr)
v = 30 km / 1.74 hr
v = 17.2 km/hr
Answer:
Given that,
An amount of $23,000 is borrowed for 11 years at 6.75% interest, compounded annually.
To find the Amount paid back after 11 years.
Explanation:
we know that,
The formula to find the,
Amount after n years of interest rate r% compounded annually is,
where P is the initial amount.
Here, we have that,
P=$23,000
r=6.75
n=11
Substitute the values we get,
Solving this we get,
Round to the nearest dollar.
Answer is: Amount paid back is $47182 after 11 years
